Doctored Cake Mix Plus Cake Mix

I need to bake a cake to fill a 9x13 (2 inch deep) cake pan (7 cups batter approx). I usually do Sharon Zambitos doctored cake mix which calls for the addition of a pudding mix. However, on hand I only have one chocolate flavoured pudding mix and the nearby grocery stores dont have anymore chocolate flavoured pudding mixes!!

Can I mix two batters (one doctored and one box) in the same pan?
I have a vanilla pudding packet but I dont think I could mix that in- right? For chocolate cake it should be in a coordinating flavor!